Have you ever heard of the Collatz conjecture? Just in case you haven't, I'll summarize it for you! Take any positive integer $n$, if it is even then simply divide it by $2$; however, if it is odd, multiply it by $3$ and add $1$. With that out of the way, I recently had the delightful idea of implementing this conjecture in a $3$x$3$ grid and having it influence adjacent cells:
The rules of the grid a pretty simple:
- Only the central cell is populated to start with.
- Tapping a cell will apply the conjecture to the targeted cell.
- Tapping a cell will apply the conjecture to all adjacent cells.
- Tapping a cell will activate all inactive adjacent cells with half of the invoking cell's value.
- The answer will define a strategy that ensures the minimum number of moves will be used for any starting $n$. 
- If you tap on a $1$, any inactive adjacent cells will remain inactive.
1: The minimum number of moves for any $n$ cannot be easily defined due to the nature of the conjecture. However, a strategy can be employed that finds the minimum number of moves for any $n$.
What is the minimum number of moves, for any positive integer $n>1$, that will ensure every cell contains a $1$?
Note: An interactive version of this puzzle exists for your convenience.